Is it permissible to supplicate that Allah unite a young man who died as a martyr with the girl he intended to propose to, as a married couple in Paradise? And are there any other deeds to achieve this?

There is no religious impediment for a woman to pray to be married in Paradise to a specific person. However, it is better for a woman to busy herself with what is beneficial and useful, for she does not know where the good lies for her.